Question

The radius of the circle $x^2+y^2-5x+2y+5=0$ is

• A. $2$
• B. $1$
• C. $\frac{3}{2}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{3}{2}$

Given the equation of the circle is $x^2+y^2-5x+2y+5=0$ can be written as

or $x^2+2.\frac{5}{2}x+\frac{25}{4}+y^2+2.y.1+1+5-1-\frac{25}{4}=0$

or ${(x+\frac{5}{2})}^2+(y+1{)}^2+4-\frac{25}{4}=0$

or ${(x+\frac{5}{2})}^2+(y+1{)}^2=\frac{9}{4}$

or ${(x+\frac{5}{2})}^2+(y+1{)}^2={\left(\frac{3}{2}\right)}^2$.

From this equation it is clear that the centre of the circle is $(-\frac{5}{2},-1)$ and radius is $\frac{3}{2}$.